A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, and choose again. What is P(red,then blue)?
A. 77/164
B.19/41
C.90/1681
D. 45/41
P(red, then blue)
= (9/41(10/41)
= 90/1681
To find the probability of choosing a red marble, replacing it, and then choosing a blue marble, you need to follow a few steps:
Step 1: Find the probability of choosing a red marble on the first pick.
There are a total of 41 marbles in the bag (7 green + 9 red + 10 orange + 5 brown + 10 blue). So, the probability of choosing a red marble on the first pick is 9/41.
Step 2: Since the marble is replaced, the total number of marbles remains the same, and the probability of choosing a blue marble on the second pick is also 10/41.
Step 3: To find the probability of both events happening, you multiply the probabilities from step 1 and step 2:
P(red, then blue) = P(red) * P(blue) = (9/41) * (10/41) = 90/1681
Therefore, the correct answer is C. 90/1681.